The role of the vortical phase in the initial structure of the wave field of a laser beam propagating in the turbulent atmosphere in statistical regularities of beam wandering is studied. It is found that in the near diffraction zone the variances of wandering of the vortical beam and the fundamental Gaussian beam turns out to be identical, if the initial radius of the Gaussian beam is equal to the radius of the ring intensity distribution of the vortical beam. In the far diffraction zone, the vortical beam wanders more slightly than the Gaussian beam with the same effective radius of the initial intensity distribution does. It is also shown that laser beams with the initial ring intensity distribution similar to the intensity distribution of a vortical beam, but not having the vortical phase distribution, are less resistant to the atmospheric turbulence than the vortical beam.
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